Calculus Questions
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
Calculus
Differential equationsFind the solution of the simultaneous linear differential equations dx dt dy 2x2y 4e 2t dt that satisfies the initial conditions 0 7 y 0 4 5x 3y 17e 2t

Calculus
Definite IntegralsSuppose that f is the function given in the graph below and that f is a piecewise function whose parts are either portions of lines or portions of circles as pictured 6 3 4 3 A 6 2 A 1 1 6 5 4 3 2 1 2 3 5 6 Let A be the function defined by A 2x f t dt b Compute the followings 5 q a What does the Second FTC tell us about the relationship between A and f Write an equation to describe the relationship 0 1 pt 30 29

Calculus
Definite Integralsroblem 3 Evaluate the following integral Problem 3 3 6 cot x In sin x dx Enter yo as in the

Calculus
Application of derivativesProblem 6 Find the arc length of the following function on the given interval f x 4 24 1 4x n 1 x 2 Enter your answer as an exact fraction or as a number correct to 4 decimals

Calculus
Application of derivativesProblem 7 Find an expression for the arc length of the upper half of a circle of radius 22 on the interval 0 t where 0 t 22 Problem 7 Enter your answer as a symbolic function of t as in these

Calculus
Definite Integralsroblem 1 Evaluate the following integral 4 x 2 x 5 dx Don t forget the absolute value in your answer Problem 1 Enter your answer as a symbolic function of x as in these examples Don t forget the absolute in your answer Use abs for absolute v


Calculus
DifferentiationProblem 4 Evaluate the following integral 1 2 100 Problem 4 dx Enter your answer as a sym function of x as in these examples

Calculus
Application of derivativesProblem 6 Consider the partial fraction decomposition of the following Problem 6 1 x 1 x 8 One of the terms in the partial fraction decomposition is of the form Enter your answer symbolically as in these examples B x 8 Find the value of B

Calculus
Indefinite IntegrationProblem 4 By making an appropriate substitution which of the following integrals is equal to SFR Problem 4 dx x x 9 5 2 8 A 37 sin 8 G Select de B 37 sin e cos 8 38 sin 8 de H de c f cos 8 37 sinf 8 de cos 0 37 sin 0 de D 38 sin 6 de E S de F cos 0 37 sin 8 cos 8 38 sin 8 S


Calculus
Definite IntegralsProblem 3 Evaluate the following integral dx 1 x 16 A j 7 16 is arctan C B 16 Tarctan f C 2 16 arctan C 2 2 D 16 1 6 arctan C E 16 1 arctan C F 16 arctan C 16 16 arctan C H 216 arctan C G Problem 3 Select

Calculus
Indefinite IntegrationProblem 2 By making an appropriate substitution which of the following integrals is equal to tan x sec 0 x dx Problem 2 A u 1 u du B x 1 u du C us 1 u 6 du D u 1 u du E u 1 u du F u 1 u 4 du G u 1 u 5 du H u 1 u du hs Select

Calculus
DifferentiationProblem 5 Find the remainder after performing the following divis 11x 5x x 5 Problem 5

Calculus
Application of derivativesA rectangle is inscribed with its base on the x axis and its upper corners on the parabola y 5 x What are the dimensions of such a rectangle with the greatest possible area Width Height 15 3 10 3

Calculus
Limits & ContinuityThe data in the table below represents the percentage of patients who have survived after diagnosis of advanced stage breast cancer at 6 month intervals of time Time after Diagnosis years 0 5 1 1 5 2 2 5 3 3 5 Percentage Surviving 95 8 83 4 74 0 58 7 46 6 40 9 32 2 a Using a graphing utility build an exponential model from the data y 120 5681 0 6918 Type integers or decimals rounded to four decimal places as needed b Express the function found in part a in the form A t Aet where t x A t Type integers or decimals rounded to four decimal places as needed

Calculus
Vector CalculusLet u 5 4 and v 4 6 Find the a component form and b magnitude length of the vector 5 12 13 13 a 5 13 12 13 V

Calculus
Application of derivativesK 5 9 A strain of bacteria is placed into a petri dish at 30 C and allowed to grow The following data are collected Theory states that the number of bacteria in the petri dish will initially grow according to the law of uninhibited growth The population is measured using an optical device in which the amount of light that passes through the petri dish is measured Complete parts a e Time hours x 0 25 3 5 4 5 6 HO Population y 0 27 0 53 0 76 1 03 1 46 A strain of bacteria is placed into a petri dish at 30 C and allowed to grow The following data are collected Theory states that the number of bacteria in the petri dish will initially grow according to the law of uninhibited growth The population is measured using an optical device in which the amount of light that passes through the petri dish is measured Complete parts a e Time hours x 0 2 5 35 45 6 Population y 0 27 0 53 0 76 1 03 1 46 CCC a Treating time x as the predictor variable use a graphing utility to fit an exponential function to the data yab 0 2698 1 3328 Round to four decimal places as needed b Express the function found in part a in the form N t Noe where x t N t 0 26980 28731 Round to four decimal places as needed c Graph the data together with the exponential function found in part a or part b on a scatter diagram Which graph correctly illustrates the exponential model found for this data Question 1 5 9 1 GC Part 4 of 5 Q NEUV ZUBOE Round to four decimal places as needed c Graph the data together with the exponential function found in part a or part b on a scatter diagram Which graph correctly illustrates the exponential model found for this data G 200 G i C E HW Score 8 33 1 of 12 points Points 1 of 5 d Use the exponential function from part a or b to predict the population at x 7 hours 0


Calculus
Application of derivativesThe financial director of a hotel finds that the income stream measured in thousands of dollars varies depending on the season She estimates that the total income can be modeled using the continuous distribution f t t 361 288t where t is measured in months What is the total income in the first year Give your answer in thousands of dollars to the nearest thousand dollars Provide your answer below

Calculus
Indefinite IntegrationA company models its income in thousands of dollars using the conti f t 20e 0 0251 12 where t is measured in months Which of the following denotes the correct formula to find the total income derived in the second year Select the correct answer below 24 O TI 20e 0 0251 1 2 dt 12 TI 2 20e 0 025r 2 dr 20e 0 025t dt O TI 36 O TI 2 20e 0 025z 2 dt O

Calculus
Application of derivativesA strain of bacteria is placed into a petri dish at 30 C and allowed to grow The following data are collected Theory states that the number of bacteria in the petri dish will initially grow according to the law of uninhibited growth The population is measured using an optical device in which the amount of light that passes through the petri dish is measured Complete parts a e Time hours x 0 2 5 3 5 4 5 6 Population y 0 27 0 53 0 76 1 03 1 46 a fialny w a as the pituition and the a graping unity to in an OAUTOT CE to o to y ab 0 2698 1 3328 Round to four decimal places as needed b Express the function found in part a in the form N t Noekt where x t N t 0 2698e0 2873t Round to four decimal places as needed c Graph the data together with the exponential function found in part a or part b on a scatter diagram Which graph correctly illustrates the exponential model found for this data A OB O C 1 2 0 2 0 2 Q Q Q Q Q

Calculus
Definite IntegralsWhat is the value of the definite integral exact fraction if necessary Provide your answer below 3 1 2 21 1 2 di Enter your answer as an

Calculus
DifferentiationLet A z f t dt with f x shown in the graph below 0 st 4 3 2 1 2 3 At what x values does A x have a local max x At what x values does A x have a local min x Restrict your answers to values 0 x 6

Calculus
Application of derivativesIf q r S d r cost t2 cos 5 0 2r dt then syntax error Question Help Video Add Work X

Calculus
Application of derivativesLet f x 5e 2 3 3 1 1 6 de t dt 0 1 List all values of x for which f x has a local maximum X

Calculus
DifferentiationGiven At what value of x does the local max of f x occur x f x S a At what value of a does the local min of f x occur x t 5t 24 1 cos t dt







Calculus
Application of derivativesFind the derivative of y with respect to x t or 0 as appropriate In x x6 27 y A 1 6ln x x12 B 6ln x 1 x7 1 6In x x7 D 1 6lnx x12

Calculus
Application of derivativesNext question 17 If f x t Get a similar question You can retry this to dt then f x 17 Hint Remember that f a t d 1 to to dt 17 Find the derivative of g a sin 1 dt g x sin x

Calculus
Application of derivativesAnswer the following questions about F x x 43x 486 B Graph F x and use geometric formulas to calculate the area between the graph of F x and the x axis from x 10 and x 15 Choose the correct graph below 20 10 15 OB 60 40 20 10 20 OC 20 10 10 20 Q OD 1000 500 50 100

Calculus
Application of derivativesind the derivative of the function 25 r sec 0 tan 0 2 A 2 sec 0 tan 0 3 tan2 0 sec 0 tan 0 C 2 sec 0 sec 0 tan 0 2 B 2 sec 0 tan 0 sec 0 D 2 sec 0 tan 0 3

Calculus
Application of derivativesUse geometric formulas to find the unsigned area between the graph of y f x and the x axis over the indicated interval f x x 8 2 9 The area between f x and the x axis is Type an exact answer using a as needed


Calculus
Application of derivativesFind the critical point s of the function f x y y6 6xy 12x and determine whether each is a local maximum local minimum a saddle point or none of these Enter the critical point s as point s a b Number of critical point s Choose one

Calculus
Application of derivativesCurrent Attempt For f x y A x Bx y Cy what values of A B and C give f x y a local maximum value of 17 at the point 6 7 A B C i

Calculus
Application of derivativesFind an equation for the tangent to the curve at the given point 20 f x 8 x x 9 64 9 A y x 9 B y 9 C y x 41 1 D y x

Calculus
DifferentiationFor f x y A x Bx y Cy what values of A B and C give f x y a local maximum value of 17 at the point 10 2 A B C i i Bul i

Calculus
Definite IntegralsT 1 A graphing calculator is recommended Sketch the region enclosed by the given curves 1 x3 y y 1 x2 0 5 0 5 y 1 0 0 5 0 5 1 0 y 1 0 0 5 0 5 0 5 0 5 1 0 1 0 M 0 5 0 5 al y 1 0 0 5 y 1 0F 0 5 1 0 0 5 0 5 JS Secti 0 5 0 5 1 0 1 5 1 0 2 0

Calculus
Application of derivativesetermine where the given function is concave up and where it is concave dow 19 f x 4x x3 A Concave up on 0 concave down on 0 B Concave up on 0 and 1 concave down on 0 1 C Concave up on 0 concave down on 0 D Concave down for all t

Calculus
DifferentiationT S S Sketch the region enclosed by the given curves y 3 x y 12x Y 3 6 1 y 8 2 X 0 3 4 82 M 6 th y 8 JS Secti MacBook Air 2 dh 3

Calculus
DifferentiationFind the extreme values of the function and where they occur 17 y 1 x2 1 A None B Local maximum at 0 1 C Local maximum at 1 0 local minimum at 1 0 D Local maximum at 1 0 local minimum at 1 0

Calculus
Indefinite Integrationy 3 M al JS Secti al ah Sketch the region enclosed by the given curves Decide whether to integrate with respect to x or y Draw a typical approximating rectangle y ex y x 1 x 1 x 1 y 3 5 2 0 webassign net y 3 y MacBook Air

Calculus
Definite IntegralsFind the area of the shaded region y 3 2 1 1 1 5 10 y x y XIT 15 20 X 27 25 PERM X

Calculus
Limits & ContinuityAtte Sketch the region enclosed by the given curves x 9y2 x 2 7y 1 0 y 0 5 0 5 1 0 1 0 0 0 5 0 5 8 1 0 M 1 0 0 5 0 5 y 1 0 1 0 0 5 webassign net JS Secti y 8 MacBook Air 6 8 0 5 1 0 X